Perturbation of semi-linear evolution equations under weak assumptions at initial time

Abstract

We prove perturbation results for abstract semi-linear
evolution equations in a Banach space. The main feature is that
only very weak assumptions are needed at initial time. This allows
to prove weak continuity properties and to deal with rather
general domain perturbation problems for semi-linear parabolic and
hyperbolic boundary value problems with various boundary
conditions. The theory also implies the well known theory on
parameter dependent equations.